4.3.1. Casual Loop Diagrams (CLD)

The possibility of developing simulation models for production and maintenance management starts from the knowledge of the interrelations between its elements. Using casual loop diagrams (CLD), the effects of the changes of certain factors in their dependent parameters are shown. Five CLDs are developed from production management to maintenance planning. Figure 8 shows the CLD for the production system as an example:

**Figure 8.** CLD for the production system.

#### 4.3.2. Methodology, Assumptions and Comparison Conditions

The aim of the simulation is to observe the impact of the delay in decision-making in a chain of manufacturing processes from the steel stamping process to the end of assembly in the automotive industry. The hypothesis is that a simulation model applying the VSM will present better results in terms of study parameters compared to the one that does not apply the VSM or that has delays in internal decision-making. The methodology for the simulation design is:


First, assumptions are defined to simplify the model with focus on the simulation goal:


Some elements are equal in all models to make possible a comparison between the models under the same conditions:


## 4.3.3. Key Performance Indicators (KPIs) for the Simulation Model

The objectives can be qualitative or quantitative. The research goal is to study the behavior of the different models in different situations of demand and configuration of maintenance and production areas. The results are quantified to evaluate the response according to the following key performance indicators:


#### 4.3.4. Definition of the Production Flow in the Simulation Model

The production process consists of a process from steel stamping to the final revision shop. The plants in the process are shown in Figure 9:

**Figure 9.** Simulation production flow (own elaboration).

*Materials* **2018**, *11*, 1346


All of them are in different shops and have production and maintenance units associated to each one of them.

4.3.5. Design of the Intra-Organizational Simulation Model for Production and Maintenance Management

As shown in Figure 10 the model is designed according to the following criteria:


**Figure 10.** Ishikawa Diagram of Hypothesis for the simulation model (own elaboration).

#### 4.3.6. Simulation Model Validation

The validation of the simulation models can be done using different methods. In this process, some simulation variables will be used to observe their behavior and to evaluate if the models will be validated. Sterman defined 12 possible methods to validate system dynamics models [42] (p. 6). One of them, the test of extreme values, is used to validate the simulation model that shows that the response of the model is plausible when taking extreme values for different input parameters. For all models, the same input and output variables are chosen to analyze and validate the models. These input variables are the total number of employees, the initial stock in work in progress (WIP) and the production strategy, make-to-order vs. make-to-stock.

• For a lower number of employees, production on time (%) must be lower and the total stock should be higher because the production facility provides more products than employees can process. Moreover, utilization of shop capacities should be lower and therefore also the production output.

As shown in Figure 11, it can be observed how the model behaves as expected. With 20 employees of maintenance and production per shop, the results for production on time (%) are 25% higher than with 15 employees and 50% higher than with 10 employees. In addition, total production and capacity utilization are higher for 20 employees than for 15 or 10 employees. Finally, cumulated stock over time is higher for 10 employees than for 15 and 20 employees because, with a lower number of production and maintenance employees, production volumes decreased.

**Figure 11.** Validation with extreme values: number of employees.

• For higher initial stocks in WIP (work in progress) at initial time, production on time (%) must be higher and total stock should be higher in the first weeks because the production facility has more products within production process at the beginning. Moreover, utilization of shop capacities should be higher and therefore also the production output in the first weeks. Afterwards, due to the CONWIP method, the production WIP converges to a CONWIP goal that is equal to one week of demand and therefore all other indicators also converge.

In Figure 12, it is shown the model results for 500, 300 and 100 WIP products as initial WIP stocks in all intermediary stocks. The results show how initially the total stock, capacity utilization, production on time and total production at the beginning are higher for 500 WIP products at initial WIP; however, after 20–40 days, all of these performance indicators are equal for all set-ups of the initial WIP stock because the model initiates production of more products if the initial stock is low due to the CONWIP method set-up.

**Figure 12.** Validation with extreme values: WIP Initial stock.

• For a make-to-order production, it is expected to have less stock during the production process, less capacity utilization and production output as well as less production on time than with a make-to-stock production.

As shown in Figure 13, it can be seen how the model results are as expected. In a make-to-order production stock, the stock after painting is lower than in make-to-stock production. Capacity utilization is 20% lower for make-to-order than for make-to-stock. Total production is higher for make-to-stock than for make-to-order because, in this configuration, only the customer orders are produced and if these orders are lower than the capacity, the extra-capacity is not utilized. Moreover, in a make-to-stock production, more products are served on time.

The model is validated because logical expected values are obtained for three different input parameters influencing multiple key performance indicators of the simulation.

**Figure 13.** Validation with extreme values: Make-to-order vs. Make-to-stock.

#### 4.3.7. Scenario Definitions

Four case studies are proposed in which two different model configurations are simulated, trying to reflect the importance of decision-making. The VSM model takes earlier these decisions and therefore can benefit earlier from the new production system configuration:

